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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$L_{p}$ smoothness and approximate continuity
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by Michael J. Evans and Paul D. Humke PDF
Proc. Amer. Math. Soc. 92 (1984), 258-262 Request permission

Abstract:

It is known that a measurable smooth function can have only countably many points of discontinuity. A measurable function is constructed here having the property of being ${L_p}$ smooth and having uncountably many points of ${L_p}$ (in fact, approximate) discontinuity.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 258-262
  • MSC: Primary 26A15
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754715-7
  • MathSciNet review: 754715